Since his last update that can be loaded via PS4 Browser and PS4 Exploit Host, today PlayStation 4 GTA V modder david1337hax announced the release of Lamance Mod Menu v0.8 via NGU for PS4 jailbroken consoles on 4.05 and 4.55 Firmware versions followed by Lamance v5.05 support. 
Download: Lamance_08_AllInAll.zip (950.36 KB) / Lamance_and_Trainer_505.zip (329.06 KB) / PS4-Lamance_127_505.bin (1.02 MB) / Lamance_405_127.bin (1.02 MB) / PS4-Lamance_127.bin (1.02 MB - Fixed Menu) / Lamance_455_405.zip (631.9 KB - PS4-Lamance_127_505.bin) / Lamance_672_132_.bin (1.02 MB - Lamance Menu v0.8 for 1.32 on PS4 6.72) via david1337hax / Lamance_672_132_fixed.bin (1.02 MB - Lamance Menu v0.8.1 for 1.32 on PS4 6.72) via david1337hax
Here's what is new from the Lamance PS4 Mod Menu 0.8 changelog included in the file download above:

PS4 GTA V Lamance Mod Menu v0.8 by seanp2500
Spoiler
Testing: NotAnotherMenu PS4 Mod Menu on 1.27 (FW 5.05) by david1337hax
Download: NotAnotherMenu_127_505.bin (1.04 MB)
Download: PS4-Lamance_127_505.bin (1.02 MB)
Download: Lamance_08_AllInAll.zip (950.36 KB) / Lamance_and_Trainer_505.zip (329.06 KB) / PS4-Lamance_127_505.bin (1.02 MB) / Lamance_405_127.bin (1.02 MB) / PS4-Lamance_127.bin (1.02 MB - Fixed Menu) / Lamance_455_405.zip (631.9 KB - PS4-Lamance_127_505.bin) / Lamance_672_132_.bin (1.02 MB - Lamance Menu v0.8 for 1.32 on PS4 6.72) via david1337hax / Lamance_672_132_fixed.bin (1.02 MB - Lamance Menu v0.8.1 for 1.32 on PS4 6.72) via david1337hax
Here's what is new from the Lamance PS4 Mod Menu 0.8 changelog included in the file download above:
- removed stats editor testings
- renamed "the something mod" -> "Dab Mod"
- improved human torch
- fixed world multiplier
- fixed button registrations
- added animation settings
- added dirt level for cars
- added burst tyres
- added drive through walls
- added vehicle vortex gun
- added shoot blocks
- added traffic lowrider mode
- added your heading (car spawn)
- added random entity (weapon)
- added advanced aimbot
- added toggle doors (veh)
- added make it rain (moneyrain)
- added minimenu
- added super haxxor
- added clown's gun
- added 2 more protections
- added vehicle weapon types
- added locally invisible
- added i am rich
- added bomb wp
- added remove attachments
- added title movement (lol)
- added vehicle hovermode
- added get ps4 time
- added ps4 build time, date, version
- added rain fx intensity
- added cloud hat opacity
- added rockstar ps4 options
- added draw blip gun
- added quick alpha
- added show talkers
- added full model changer
- added full components list
- added lotto
- added advanced boost
- added easy spawner (car)
- added location money drops
- added dubstep gun
- added full ptfx list
- added add mp cash
- added drop vehicle health / armor
- added make vehicle storable
- added disable vehicle horn
- added vehicle rainbow neons
- added vehicle police mode
- added radio options
- added object weapon bypass
- added get headshot
- added ped components
- added red pulse
- added walk clip (advanced / funny version of noclip)
- added with preview vehicle spawner
- added mini-lamance
- added superman fists
- added super rhino
- added aggressive people mod
- david1337hax - developing the menu
- vicodin10 - some help & a lot of testing
- j0n4s_sincemodz - testing the menu on 4.55
- RSPxAndrew2007x - testing the menu on 4.55
- ignacio1420 - testing the menu on 4.05
- john1337hax - dank name
- 2much4ux - native caller, some help & debug settings for 4.55
PS4 GTA V Lamance Mod Menu v0.8 by seanp2500
Spoiler
Testing: NotAnotherMenu PS4 Mod Menu on 1.27 (FW 5.05) by david1337hax
Download: NotAnotherMenu_127_505.bin (1.04 MB)
Download: PS4-Lamance_127_505.bin (1.02 MB)